Glass sheets produced with a down draw process, such as a fusion down draw process or a slot draw process, typically begin by producing from a molten glass material a glass ribbon that descends from a forming body. The glass ribbon is subsequently cut or separated into individual glass sheets at a location where the glass of the ribbon has been sufficiently cooled, and a viscosity reached where the ribbon has entered into an elastic state. More simply stated, the portion of the ribbon where the separation takes place is considered to be a solid. However, as the glass ribbon descends from the forming body the ribbon width has a tendency to attenuate and the edge portions of the ribbon thicken. These thickened edge portions are commonly called beads. Separating the glass ribbon across these thickened portions has proven difficult, and results in a large release of energy that can propagate upward toward the region of the glass where the glass transitions from a viscous material into an elastic solid. This energy release can result in the formation of residual stress and possible deformation of the resultant glass sheets.